<img src="/images/picture.jpg" /> is a relative link (it is relative to the location of the doccument that contains it), not an absolute link.

If you copy the directory structure to the developement server, you shouldn't need to change any links if they are all relative. Of course, this would mean placing all of this clients website files on the root of your dev server though.

I hate to correct someone in Public but Zagga is wrong.
<img src="/images/picture.jpg" /> is not based on the current directory but on the Document Root directory for the web site. For example all the sites on my server are located in /var/www/html/ and have their own directory by domain. My web site resides in /var/www/html/txlinux.com/ which is listed as the document root for the site I can refer to any file in the top directory of the site with <img src="/picture.jpg" /> but the absolute path for the files on the server is /var/ww/html/txlinux.com/picture.jpg. The only time I really need to use this form of the path is when using "Include file.php (i.e. Include /var/www/html/txlinux.com/config/config.php )

The example I used (<img src="/images/picture.jpg" />) is not an absolute URL (because it is not the full, unique address to the file) but it does act like one because the first "/" is an instruction to start at the server root, no matter where the current document is.